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## Homework Statement

Evaluate ∫

_{c}(x + y) ds, where C is the circle centred at (1/2, 0) with radius 1/2.

## Homework Equations

## The Attempt at a Solution

parametrise

x=1/2cos(t)

y=1/2sin(t)

0≤t≤2π

ds=√dx

^{2}+dy

^{2}

=√(1/2)

^{2}-sin

^{2}(t)+(1/2)

^{2}cos

^{2}(t)

=√-(1)

^{2}(1/2)

^{2}sin

^{2}(t)+(1/2)

^{2}cos

^{2}(t)

=√-(1)

^{2}(1/2)

^{2}(sin

^{2}(t)+cos

^{2}(t))

ds=1/2

∫ [(1/2)cos(t) + (1/2)sin(t)]*(1/2) dt, where 0≤t≤2π

I evaluated this integral and got 0. Is this because C is a simple closed curve?